Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A baker uses 1/3 of a bag of sugar for one cake and 1/4 of the same bag for another cake. What fraction of the bag of sugar is left if the bag originally contained 5/6 of its full capacity?
- A1/12
- B1/4
- C1/3
- D1/6
Show answer & explanationAnswer & explanation
Correct answer: B. 1/4
First, find the total sugar used: 1/3 + 1/4. To add these, find a common denominator, which is 12. So, 4/12 + 3/12 = 7/12. Next, subtract the used sugar from the original amount in the bag: 5/6 - 7/12. Convert 5/6 to 10/12. Then, 10/12 - 7/12 = 3/12. Simplify the fraction: 3/12 = 1/4.
Why the other options are wrong
- A. This might result from an arithmetic error or an incorrect common denominator.
- C. This might result from a calculation error, perhaps subtracting the wrong way or simplifying incorrectly.
- D. This might be the result of a calculation error after finding the common denominator.
Fraction Addition and Subtraction
To add or subtract fractions, they must have a common denominator. Once common denominators are established, add or subtract the numerators and keep the denominator the same.
- Find the Least Common Multiple (LCM) for the denominators.
- Convert each fraction to an equivalent fraction with the common denominator.
- Perform the addition or subtraction on the numerators.
- Simplify the resulting fraction if possible.
Memory trick: Common ground for the bottom, then add/subtract the top!